ܢௐѯੱଆაಪܢಃᆣקࡎ Stock Volatility Models and the Pricing of Warrants ਟݚ ᆢᆒ மѰ č༰ն࿐ࣜ࠶࿐ჽࣁವ༢đ༰ն࿐ଲࣜ࠶࣮ჽđ361005Ď 2005୍10ᄅֻ၂۠ ଽಸᅋေğЧ໓ᄝؓଢభӈႨ֥ᇙ؟ѯੱଆࣉྛൌᆣٳ༅֥ࠎԤഈđЧ໓০ႨHong & Li č2005Ď٤ҕඔଆഡקဒٚمđбࢠ۲۱ଆ֥ഡק༂ҵđ࿙ᅳԛଆഡק༂ҵቋཬ֥ଆbᄝᅧѓ֥ܢௐࡎ۬ѯੱหᆘᆭުđ০Ⴈหवઅଆඌؓؓᇏݓܢಃٳᇂުഈ൧ؿྛ֥൮ᆦ܄ඳಪܢಃᆣiiЏۑಃᆣቓਔ༢֥קࡎ࣮bЏۑಃᆣࣉྛקࡎbקࡎࢲݔіૼđЏۑಃᆣ֥൧ӆࡎ۬ૼཁФۚܙđၩሢॖିթᄝбࢠᇗ֥൧ӆࠏགྷའbЧ໓ࢲކݓห൹֥ᇅ؇МࣟđؓՎࣉྛਔࡥေ֥ٳ༅ѩิԛཌྷႋ֥ᆟҦࡹၰb ܱՍğಪܢಃᆣa๋ᄁଆatٳ҃aഡקဒ Abstractğ This paper used a lot of popular volatility models to study the dynamic behavior of underlying stock and then used Hong & Lee (2005) nonparametric specification test to compare the model specification errors of different models. Based on the result of volatility estimatiestimation, we used the Mante-Carlo simulations to price Baogang warrant, Chinese first Warrant after the reform of stock market, and compare the pricing results of different models. The pricing results showed that Baogang Warrant is seriously overpriced. There is a strong manipulation in the market. We studied some possible institutional reasons for such manipulation and proposed some policy suggestions in the end. Key Words: Warrants Pricing, Jump, t Distribution, Specification Test
1a ႄ ܢௐࡎ֥۬ѯหᆘ൞ܢௐစളӁࡎ֥۬थקྟၹbBlack & Scholes (1973) ࡌഡܢௐࡎ۬ڛՖࠫޅ҃ᄎđᄝ၂۱ส০֥ٳ༅ॿࡏ༯۳ԛਔൔ௹ಃࡎ֥۬קࡎ܄ൔbఃᇗေ֥ࡌഡ่ࡱ൞ѯੱູ၂۱ӈඔb൞ᄀটᄀ؟֥ൌᆣ࣮ࢲݔіૼđܢௐ൬ၭੱթᄝཁᇷ֥ࡕڂ٧ແགྷའđޓႨ၂Ϯ֥ᆞٳ҃ࣉྛ૭ඍđطఃѯੱթᄝૼཁ֥ൈэྟหᆘb෮ၛđ٢ॺѯੱޚק่ࡱđѩ࣮ܢௐѯੱ֥эหᆘđؓܢௐ௹ಃ֥ᆞಒקࡎऎႵᇗေၩၬđᆃ္൞ଢభܢௐ௹ಃקࡎ࣮֥၂۱ᇗေଽಸ (Duan, 1995)b ܢௐࡎ۬ѯ֥նਈൌᆣ࣮ࢲݔіૼđܢௐѯᇶေหᆘႵğč1Ďѯੱ֥ൈэྟđऎุطᇶေႵѯੱऊোིႋčvolatility clusteringĎބۗۆིႋčleverage effectĎbᆌؓѯੱऊোིႋđEngle (1982) ิԛ֥ሱ่݂߭ࡱၳٚҵčARCHĎଆđࡌק൬ၭੱҗҵڛՖ၂۱่ࡱᆞٳ҃đ่ࡱ௹ຬູਬđ่ࡱٚҵູၛభۄ௹൬ၭੱ༂ҵ֥ٚݦඔbBollerslev (1986) ᄝARCHଆᇏႄೆ౫௹༂ҵཛđ֤ܼ֞ၬሱ่݂߭ࡱၳٚҵčGARCHĎଆbᄝՎࠎԤഈđॉ੮֞ڄགၮࡎෛൈࡗэ߄طэ߄֥ၹđEngle, Lilien & Robbins (1987)ิԛਔARCH-Mଆbॉ੮֞ѯੱ֥٤ؓӫྟđNelson(1991), Zakoian (1994) ٳљิԛਔEGARCHބTGARCHଆb(2) ܢௐѯ֥ಖ๋ᄁྟbࣜ࠶֥ѯđၛࠣᇗေᆟҦaཨ༏ބ܄ۡčೂIPOđ࡙ѩ൬ܓ֩Ď֥֞টđࣜӈ߶֝ᇁࣁವሧӁࡎ֥۬նږ๋ᄁ (Ball & Torous (1983), Vlaar & Palm (1993) , Das (2002))bᆃᄝᇏݓܢௐ൧ӆႭູԛđၹູᇏݓܢ൧֥၂۱ཁᇷหׄ൞൳ᆟکᆟҦ֥႕ཙޓնbႮႿሧᆀᄝն؟ඔ౦ঃ༯ѩ҂ିყҩᇗնᆟҦԛ֥ൈࡗၛࠣᆟҦ֥৯؇đᆟҦؓܢ൧֥႕ཙॖႮ๋ᄁ (Jump) ၹሰট૭ඍbč3Ďܢௐ൬ၭੱٳ֥҃٤ᆞྟbܢௐ൬ၭੱऎႵૼཁ֥ࡕڂ٧ແགྷའđބᆞٳ҃Ⴕሢཁᇷ֥ҵၳđູՎླေႄೆ၂ུ٤ᆞҗҵٳ҃ট૭ඍࣁವඔऌ֥ᆃ၂หᆘbᄝࣁವൈࡗਙᇏቋӈႨ֥٤ᆞҗҵٳ҃Їওtٳ҃ބܼၬ༂ҵٳ҃ (GED)b ݓܢௐ൧ӆ൞၂۱ྍྖ֥ܢௐ൧ӆđစളӁ൧ӆᆞᇯ҄ؿᅚఏটđೂ܄ඳಪܢಃᆣၘࣜᇗྍषഈ൧ࢌၞbೂޅᅳ֞ѓ֥ሧӁࡎ۬ѯ֥ܿੰđطؓಪܢಃᆣሙಒקࡎđ҂ࣇ߶ؓଢభ൧ӆӁളᆷ֝ၩၬđѩ߶ؓၛުݓଽᇯ҄ؿᅚ֥စളקࡎקਅݺ֥ંࠎԤbಖطđଢభݓଽ࿐ࢸෙႵཌྷ֒؟ᆌؓܢௐ൧ӆѯੱ֥࣮ӮݔčᄃӔ (2001)đౄ (1994), ఃૼ֩ (1998), νྖ֩ (1998), Ӊڌ (1999), ᅦනఅ֩ (2000)Ďđ൞๙ݖ༢ֹ࣮ѓ֥ሧӁࡎ۬ѯੱหᆘđࣉطࡼᆭॉ੮ࣉ௹ಃקࡎᇏ֥࣮ଢభߎޓഒടࠣđᆃ္ᆞ൞Ч໓ᇶေ֥࣮ࠏb ᄝؓಃᆣࣉྛקࡎ֥ݖӱᇏđંഈླေॉ੮ಃᆣᆳྛൈؓѓ֥ܢௐӁള֥ܢಃ༎ቔႨđࣉطླေؓ௹ಃקࡎݖӱᇏ֥ܢࡎࠣఃѯੱࣉྛྩᆞbಖطđᆌؓಃᆣקࡎᇏܢಃ༎ིႋ֥նਈ࣮іૼčGalai & Schneller (1978), Schulz & Trautman (1989,1994)đCorunhy & Galai (1991)Ďđ༎ིႋؓൌ࠽קࡎࢲݔ႕ཙѩ҂ૼཁĠѩđંھಃᆣ෮ି༎ܢಃ֥ਈ؟նđᆺေ҂߶ᄝࢤ࣍ᆳྛರൈಯԩႿᇗྴᆴሑđࣼॖၛᆰࢤᄎႨીႵྩᆞ֥௹ಃקࡎٚمؓఃࣉྛקࡎb Ч໓ᇶေᄎႨ۲۱ѯੱଆؓѓ֥ሧӁ֥൬ၭੱਙࣉྛކđಖުбࢠ۲ଆࢲݔđቋުࡼଆҕඔ֥ܙ࠹ࢲݔᄎႨ֞ಪܢಃᆣ֥קࡎᇏbૌ෮ॉ੮֥ଆෛࠏႳሼଆaGARCHቂଆđ๋ᄁଆၛࠣtٳ҃ଆbູਔбࢠ҂ଆ֥ഡק༂ҵđૌႨHong & Li (2005) ٤ҕඔଆഡקဒbູਔؓ۲ᇕѯหᆘ༯֥ಪܢಃᆣקࡎđૌႨหवઅଆbቋުđᄝՎקࡎࠎԤഈđࡼᄎෘࢲݔაൌ࠽൧ӆࡎ۬ࣉྛбࢠđٳ༅֝ᇁࡎ۬ҵၳ֥۲ᇕჰၹb Ч໓܋ٳູੂ۱҆ٳđֻؽ҆ٳࡥေࢺകૌ෮ॉ੮֥֞۲ᇕѯଆၛࠣHong & Lič2005Ď٤ҕඔଆഡקဒٚمĠֻ҆ٳ০Ⴈൌ࠽ඔऌܙ࠹۲۱ଆ֥ҕඔѩᄝՎ
ࠎԤഈࣉྛ٤ҕඔଆഡקဒđбࢠ۲۱ଆ֥ഡק༂ҵĠֻඹ҆ٳᄎႨหव୶ଆؓЏۑಃᆣࣉྛקࡎĠֻ҆ٳϜંקࡎა൧ӆࡎ۬ࣉྛбࢠđٳ༅ൌ࠽ࡎ۬ொ֥ᇅ؇МࣟđѩิԛᆟҦࡹၰĠֻੂ҆ٳᄵ൞၂۱ࡥ؋֥ࢲંb a ѯଆࠣ٤ҕඔଆഡקဒٚم 2ē1 ܢௐ൬ၭੱѯଆ і1ਙԛਔૌ෮Ⴈ֥۲ᇕܢௐ൬ၭੱѯଆđЇওਔଢభੀྛ֥۲ᇕଆđऎุЇওč1ĎෛࠏႳሼଆđࠧࡌഡѯੱູ၂۱ӈඔĠč2ĎGARCHቂଆđࠧѯੱ൳֞ൎྐ༏֥႕ཙ҂؎ؿളэđЇও ၂Ϯ֥GARCHଆđཋᆷඔ၍नEWMAଆđۗۆིႋTGARCHଆđၛࠣॉ੮ѯੱؓनᆴ႕ཙ֥GARCH-MଆĠč3Ď๋ᄁଆđࠧܢௐ൬ၭੱ൳֞ޡܴࣜ࠶֩۲ᇕؿ൙ࡱ֥႕ཙ߶ؿളಖ๋֥ᄁđЇওGARCH๋ᄁଆđTGARCH๋ᄁଆၛࠣGARCH-M๋ᄁଆĠč4Ďtٳ҃ଆđࠧܢௐ൬ၭੱڛՖ٤ᆞٳ҃đЇওGARCH-tٳ҃ଆđTGARCH-tٳ҃ଆၛࠣGARCH-M-tٳ҃ଆb і1ğ۲ᇕܢௐࡎ۬ѯଆ µ(r,θ)σ(r,θ)ଆ tt(a) ෛࠏႳሼଆ µ RWσ (b) GARCHଆ µ GARCH 2đh=α+αξ+βh tt1t−11t−1µ EWMA 2đ h=λξ+(1−λ)httt−1t−1µ TGARCH 2đhα(αϕ =++d)ξ+βht1t−1−11t−1µ EGARCH 22đlnh=α+αξ/h+βξ/h+βlnhht1t−1t−11t−1t−12t−1tGARCH-M 2đµ+δh hαα =+ξ+βhtt1t−11t−1t(c) ๋ᄁ (Jump) ଆ 2GARCH µ+JdqđđJ~N(ϑ,γ)2đ =α+αξ+βhht1t−11t−1t dq~(q)2TGARCH µ+JdqđđJ~N(ϑ,γ)2đ h=α+(α+ϕd)ξ+βht1t−1−11t−1 dq~(q)GARCH 22đđJ~N(ϑ,γ)đ µ+δh+Jdqh=α+αξ+βhttt1t−11t−1 dq~(q) (d) tٳ҃ଆ
µ GARCH 2đhαα =+ξ+βhtt1t−11t−1µ TGARCH 2đhα(αϕ =++d)ξ+βht1t−1−11t−1GARCH-M 2đµ+δh hαα =+ξ+βhtt1t−11t−1tᇿğܢௐ൬ၭੱѯ֥ଆഡק၂ູğr=µ(r,θ)+ξđθіൕҕඔࠢކđξ=σ(r,θ)zbᄝଆtttttt2v+1v+1zt2Γ()(1+)(a), (b), (c) ᇏđ z~i..(0,1)Ġᄝଆ (d) ᇏđz~t(v)đb 2vttt(v)=v⎛⎞Γvπ⎜⎟2⎝⎠2ē2 ٤ҕඔଆഡקဒٚم Hong & Li (2005) ቋ࣍ิԛႨ٤ҕඔٚمটဒൈࡗਙଆഡק֥ᆞಒྟbᆃ၂ဒٚمൡႨႿ۲ᇕۀੱٳ҃ଆđЇওЧ໓෮࣮֥෮ႵѯੱଆbႮႿҐႨ٤ҕඔٚمđᆃᇕဒٚمؓ۲ᇕ۲ဢ֥ଆഡקհ༂नႵޓ఼֥ҩି৯bՎຓđဒ࠹ਈ֥ࡶ࣍ྛູაܙ࠹ҕඔ֥ඔଢބնཬܱđၹՎଖ၂ଆЇݣޓ؟ીႵࢳି৯֥эਈࣼ҂ॖି߶֒ቔቋݺ֥ଆđෙಖ֥රಖᆴॖିቋնbHong & Li (2005) ဒ࠹ਈၹՎॖၛФ൪ູޙਈଆᆞಒྟ֥၂۱ѓԄbဒ࠹ਈᄀཬđіૼھଆࣼᄀࢤ࣍ᆞಒഡקb ഡ൬ၭੱਙູ{r}đႨP(x,t|y,s)іൕrᄝsൈख़֩Ⴟyđᄝtൈख़֩Ⴟx֥ሇ၍t0tૡ؇इᆔbଆഡקဒಪູೂݔ၂۱ଆഡק൞ᆞಒ֥đᄵ၂קթᄝҕඔθ∈θ֤0{p(x,t|y,s,θ)=P(x,t|y,s)}ࠫެԩԩӮ৫b 00nܴؓҩਙ{r}ࣉྛࠒٳэ߄đקၬ၂۱֥ਙZ(θ) τ∆τ=1trτ∆ Z(θ)=p(x,τ∆|x,(τ−1)∆,θ)dxτ=1,",nτ(τ−1)∆∫−∞ೂݔଆഡקᆞಒđᄵ၂קթᄝҕඔθ∈θ֤{p(x,t|y,s,θ)=P(x,t|y,s)}ࠫެ000nԩԩӮ৫đࠧ{Z=Z(θ)}൞(0,1)đᆃ൞၂۱৳ކࡌഡဒbHong and Li (2005)ττ0τ=1๙ݖбࢠਆ۱U(0,1)эਈ{Z,Z}֥৳ކૡ؇ݦඔg(z,z)֥ނܙ࠹ˆg(z,z)ა1ᆭττ−jj12j12ࡗ֥ܱ༢ܒᄯਔਆ۱࠹ਈb ൮༵đ৳ކૡ؇ݦඔg(z,z)֥ނܙ࠹ˆg(z,z)ູğ j12j12n−1ˆˆ ˆg(z,z)=(n−j)K(z,Z)K(z,Z)12∑jh1τh2τ−jτ=j+1ఃᇏđ
1x−y⎧−1hk()/k(u)du,x∈[0,h]∫⎪−(x/h)h⎪x−y⎪−1 K(x,y)=hk(),x[h,1−h]⎨hh⎪(1−x)/h⎪x−y−1hk()/k(u)du,x∈[1−h,1]⎪∫−1h⎩11k(i)൞ᆦӪູࠢ[−1,1]֥Ⴕࢸؓӫۀੱૡ؇ݦඔđၹՎđk(u)du=1,uk(u)du=0∫∫−−12uk(u)du<∞đᄝᆃૌ࿊ᄴඹՑނݦඔğ ∫−1n1522 k(u)=(1−u)XI∑i(|u|≤1)16i=1−1/6ˆˆˆˆˆఃᇏđI൞ൕྟݦඔĠZ=Z(θ)đθ൞θ֥၂ᇁܙ࠹Ġh=SnđS൞ဢЧ(|u|≤1)ττ0ZZn{Z}֥ѓሙ༂b ττ=1ˆֻ၂ᇕဒ൞ࡹ৫ᄝˆg(z,z)ބ1֥ٚྙൔഈ֥đM(j)ູğ j121112ˆMj=gˆ ()[(z,z)−1]dzdz1j1212∫∫00ˆˆ๙ݖM(j)ܒᄯ࠹ਈQ(j)ğ 101/2ˆˆQ(j)=[(n−j)hM(j)−A]/V 1h0ఃᇏ 1−1b0−122A=(h2)k(u)du+2k(u)dudbh∫∫−0 1122V=2[[k(u+v)k(v)dv]du]0∫∫−1−1dˆᄝଆഡקᆞಒ֥౦ঃ༯đHong & Li (2005) ᆣૼQ(j)⎯⎯→Nđᄝଆഡק҂ᆞ(0,1)npˆಒ֥౦ঃ༯đࠧ{Z=Z(θ)}҂൞ࠇᆀU(0,1)đQ(j)⎯⎯→∞ ττ0τ=1 3a ൌᆣٳ༅ 1ૌ࣮֥ܢௐစളӁູЏۑಃᆣđఃѓ֥ሧӁ൞Џۑܢٺčࢌၞս600019Ďbູਔ࣮Џۑܢٺ֥൬ၭੱѯหᆘđૌႨఃՖ2002୍12ᄅ12ರ֞2005୍6ᄅ17ರ֥൬ၭੱඔऌđ܋1081۱ဢЧׄbؓਙࣉྛֆ໊۴ဒđᄝ99Ċ֥ᇂྐඣഈऋधֆ໊۴ࡌഡđਙ҂թᄝֆ໊۴གྷའđॖၛᆰࢤቔູު૫ٳ༅֥ؓའb 1ླေඪૼ֥൞đЧ໓ؓႿ၂ᆦหקಪܢಃᆣ֥קࡎٚمॖၛܼᄎႨ֞ၛުࠧࡼԛ֥ఃಪܢಃᆣקࡎᇏb
1đ2ٳљ߂ԛਔЏۑܢٺ൬ၭੱ֥ൎэၛࠣᆰٚđՖᇏᆰֹܴؿགྷ൬ၭੱ֥٤ᆞٳ҃ބޓ఼๋֥ᄁགྷའđѩႵ၂קӱ؇֥ѯੱऊোགྷའb 1ğЏۑܢٺರ൬ၭੱൎэ 2ğЏۑܢٺರ൬ၭੱᆰٚ 3ē1 ଆҕඔܙ࠹ࢲݔ ૌ࿊ᄴࠞնරಖܙ࠹čMLEĎ֥ҕඔܙ࠹ٚمđᄝܙ࠹֥ݖӱᇏ࿊ᄴ֥ෘمູBHHHđႨᄎෘೈࡱູ,ҕඔܙ࠹ࢲݔೂі2b ଆҕඔܙ࠹ࢲݔіૼğֻ၂đն҆ٳଆ֥၍ཛन൞҂ཁᇷ֥đඪૼܢࡎѯᄝ؋௹ଽޓყҩĠֻؽđႄೆGARCHིႋᆭުđଆܙ࠹֥රಖݦඔᆴႵ෮ᄹࡆđGARCHଆ֥ҕඔ္൞ཁᇷ֥đඪૼھܢௐ֥൬ၭੱਙ֥ಒऎႵ၂קӱ؇֥ѯੱऊোིႋĠֻđGARCH-MބTGARCHଆაGARCHଆཌྷбđఃරಖᆴѩીႵૼཁᄹࡆđࠧᆃུଆؓඔऌ֥ކࢲݔѩીႵڿđEWMAଆބEGARCHଆ֥රಖᆴّطࡨഒĠֻඹđᄝGARCHଆᇏႄೆ๋ᄁၹሰᆭުđଆ֥රಖᆴิۚđఃᇏ۲ଆ๋֥ᄁ఼؇ࠫެ၂ဢđᄝ1%ඣഈཁᇷđඪૼ๋ᄁ֥ಒթᄝđॖᄝ၂קӱ؇ഈႨটࢳ൬ၭੱਙ֥ࡕڂިແགྷའđ҂֥GARCHଆഡקؓކࢲݔીႵ႕ཙĠֻđᄝGARCHଆᇏႄೆ٤ᆞҗҵٳ҃ᆭުđଆ֥රಖᆴഈശđඪૼဢॖၛႨႿख़߂൬ၭੱ֥ࡕڂ٧ແགྷའđა๋ᄁଆ֥ܙ࠹ࢲݔ၂ဢđ҂֥GARCHଆഡקؓކࢲݔીႵ႕ཙb 3ē2٤ҕඔഡקဒࢲݔ ഈඍҕඔܙ࠹ࢲݔࢣൕਔЏۑܢٺܢௐ൬ၭੱਙଆ֥၂ུᇗေหᆘđࠧթᄝૼཁ֥GARCHིႋđ๋ᄁིႋၛࠣ٤ᆞྟđᆃུଆ൞ڎၘࣜቀၛख़߂൬ၭੱਙ֥ܿੰđߎླေࣉ၂ֹ࣮҄bູՎđૌࡼၛഈ۲۱ଆᄝކᇏӁള֥җҵࣉྛHong & Li (2005) ٤ҕඔଆഡקဒbဒࢲݔҕі3b ˆі3ğ۲۱ଆ٤ҕඔဒ֥Q(j)࠹ਈ ଆ j=1 j=5 j=10 ଆ j=1 j=5 j=10 RW RW-GARCH-Jump RW-GARCH RW-EWMA RW-TGARCH RW-GARCH-t RW-EGARCH RW-TGARCH-t RW-GARCH-M RW-GARCH-M-t
ˆႮၛഈࢲݔॖၛुԛğ൮༵đෛࠏႳሼଆ֥Q(j)࠹ਈޓնđඪૼթᄝޓն֥ˆଆഡק༂ҵbఃՑđᄝෛࠏႳሼଆᇏႄೆGARCHིႋၛުđଆ֥Q(j)ᆴႵ෮ࢆ֮đଆഡק༂ҵႵ෮ࢆ֮đඪૼթᄝ൬ၭੱऊোགྷའđGARCHଆಒൌିܔᄝ၂קӱˆ؇ഈࢳ൬ၭੱਙ၂ུଽᄝэܿੰbఃᇏEWMA֥Q(j)бࢠཬđඪૼބఃGARCHଆཌྷбđEWMAଆ֥ഡק༂ҵ۷ཬđᆃაරಖᆴбࢠࢲݔթᄝҵၳb൞෮ႵGARCHˆଆಯಖم๙ݖဒđඪૼಯಖթᄝଆഡק༂ҵbֻđႄೆ๋ᄁၹሰުđQ(j)࠹ਈ༯ࢆđଆഡק༂ҵննࡨഒđඪૼ๋ᄁ൞ᇏݓܢௐ൬ၭੱѯ҂ॖಌഒ֥၂۱ᇗေၹሰbఃᇏGARCH๋ᄁଆ֥ഡק༂ҵཬႿTGARCH๋ᄁଆၛࠣGARCH-M๋ˆᄁଆbֻඹđႄೆҗҵ֥tٳ҃ᆭުđ Q(j)ဢ༯ࢆđഡק༂ҵննࡨഒđඪૼ൬ၭੱਙڛՖࡕڂ٧ແ֥౦ྙ٤ӈૼཁđა๋ᄁଆোරđGARCH-tଆ֥ഡק༂ҵཬႿTGARCH-tଆބGARCH-M-tଆb൞҂ં൞๋ᄁၹሰߎ൞җҵtٳ҃đم๙ݖଆഡקဒđඪૼଆಯಖթᄝ၂ק֥ഡק༂ҵb ၹՎđ๋ᄁଆބҗҵtٳ҃ଆॖၛႵֹི૭ඍ൬ၭੱ֥ࡕڂ٧ແđࢆ֮ଆഡק༂ҵđఃڿӱ؇္նุཌྷb࿊ᄴଧ၂ᇕଆቔູЏۑಃᆣކקࡎ֥ѓሙđླေॉ੮ᇏݓܢௐ൧ӆ֥ൌ࠽౦ঃbᇏݓܢௐ൧ӆޓಸၞ൬֞ᆟҦ֥႕ཙطؿളಖྟ֥эđᆃᇕэ๙ӈ൞٤৵࿃֥đطऎႵޓ఼֥҂ॖყҩྟđၹط۷ൡކႿ๋ᄁଆbࠎႿᆃ۱ჰၹđૌၛ๋ᄁଆቔູЏۑಃᆣކקࡎ֥ѓሙđбࢠ۲۱ଆ֥קࡎࢲݔb 4a Џۑಪܢಃᆣקࡎࠣૹۋྟٳ༅ 4ē1קࡎٚمࠣࢲݔ ႮႿᇙ؟֥࣮іૼčGalai & Schneller (1978), Schulz & Trautman (1989,1994)đCorunhy & Galai (1991)Ďđಃᆣ֥༎ིႋؓקࡎࢲݔ႕ཙ҂նđ෮ၛᄝЧ໓ᇏૌ҂ॉ੮Џۑಃᆣᆳྛ෮ջট֥༎ིႋđᆰࢤᄝჰ༵ѯੱหᆘ่֥ࡱ༯০Ⴈหॉઅଆٚم2ؓЏۑಃᆣࣉྛڄགᇏྟקࡎbקࡎ֥ऎุٚمູğ༵Ⴈหवઅٚمଆԛڄགᇏྟൗࢸᇏ၂קѯੱଆ༯֥ܢௐࡎ۬ਫ਼ࣥđ০Ⴈ௹ಃ֞௹߭Б܄ൔmax(0,S−X)࠹ෘھਫ਼Tࣥ༯֥௹ಃ߭БĠᇗگഈඍݖӱ၂קՑඔđ࠹ෘૄՑਫ਼ࣥ༯֥௹ಃ߭БĠቋު࠹ෘ௹ಃ߭Б֥नᆴѩႨڄག০ੱ์གྷ֤֞ھ௹ಃ֥ކࡎ۬b࠹ෘӱ֥Ԛҕඔഡᇂೂ༯ğԚܢࡎS=đѩॉ੮२Ԣӵ୶ޣ০ჭ֥์གྷᆴĠᆳྛࡎ۬X=Ġڄག൬ၭ0ੱr=Ġקࡎൈࡗູׄఃഈ൧֒฿ (2005୍8ᄅ22ರ)đᆳྛൈࡗT=252฿ĠႻॉ੮f ֞ࡎ۬ᆦӪӵ୶đᄝಃޙᆃ۱ၹުđࡆೆਔࡎ۬҂ି֮Ⴟ4ჭ֥ཋᇅđᄎෘՑඔഡᇂູ50000Ցbקࡎ֥ࢲݔೂ༯і4a3ğ і4ğ۲۱ѯੱଆ֥௹ಃקࡎࢲݔ ଆ ௹ಃࡎ۬ ଆ ௹ಃࡎ۬ 1 RW 7RW_GARCH_jump 2ླေඪૼ֥൞đЧ໓ؓႿЏۑಃᆣ֥קࡎٚمॖၛܼᄎႨ֞ၛުࠧࡼԛ֥ఃಪܢಃᆣקࡎᇏb
2 RW_GARCH 3 RW_GARCH_EWMA 9RW_TGARCH_jump 4 RW_GARCH_M 10RW_GARCH_t 5 RW_EGARCH 11RW_GARCH_M_t 6 RW_TGARCH 12RW_TGARCH_t 3ğ۲۱ѯੱଆ෮֤ԛ֥௹ಃࡎ۬ (ޘᇠඔሳ1Ē14ٳљ၇ඨսіၛഈଆ) 8"Q)QQUU.))$NN@@@$$@8VVV.)3)33)&K"KK@$$""$@@(@@)33((3)).)$"@"&5"$$@$3(8(@@(333)3"5@88@""$"(@8338((3(@833@@"58388(@333@8833 Ⴎקࡎࢲݔॖၛؿགྷđ҂ଆ֥ಃᆣקࡎࢲݔթᄝбࢠն֥ҵၳđRWଆ֥קࡎࢲݔູđGARCHଆ֥קࡎࢲݔն҆ٳᄝᆭࡗ čᆺႵEWMAקࡎࢲݔູĎđ๋ᄁଆ֥קࡎࢲݔᄝđطҗҵtٳ҃ଆ֥קࡎࢲݔनᄝቐႷbॉ੮๋֞ᄁၹሰ֥ଆ෮קԛট֥ࡎ۬бીႵॉ੮๋ᄁݖӱ֥קࡎ֮đᄝଖᇕӱ؇ഈඪૼਔھܢௐ൬ၭੱऎႵੱޓ֮ږ؇ն఼֥ਛ๋ᄁđᆃᇕಖ๋֥ᄁ߶ᄹࡆᆜุဢЧ֥ѯੱđᇁପུીႵิ౼ԛ๋ᄁၹሰ֥ଆקࡎொۚbطđ۷ູᇗေ֥൞đଆഡק༂ҵӱ؇նุཌྷ๋֥ᄁଆބҗҵtٳ҃ଆקࡎࢲݔҵၳಏٳնbᆃіૼđᄝູ၂۱စളӁ࿊ᄴކൡ֥ѯଆቔູקࡎѓሙൈđૌ҂ࣇေܱྏھଆ֥ഡק༂ҵሑঃđ۷ູᇗေ֥൞ॉҳٳ༅ھ൧ӆ֥ൌ࠽МࣟbᆺႵࡼ࠹ਈٳ༅෮֤֥ࢲંൌ࠽౦ঃႵࠏ৳༢đҌି֤ԛбࢠॖौ֥ࢲંbᇏݓܢௐ൧ӆ൳ᆟҦ႕ཙಖ๋ᄁ֥หᆘđᄝޓնӱ؇ഈथקਔ๋ᄁଆ൞۷ކ֥࿊ᄴđၹՎಃᆣ֥ކࡎ္۬ႋھၛ๋ᄁଆ֥ࢲݔቔູѓሙb 4ē2ࡎ۬ૹۋྟٳ༅ ᄝഈ૫֥קࡎࢲݔᇏૌࡌഡڄག০ੱູ%ၛࠣܢௐࡎ֥۬ᆦӪູ4bູਔٳ༅ᆃུࡌഡؓקࡎࢲݔ֥႕ཙđૌླေࣉྛૹۋྟٳ༅b ൮༵ᄝڄག০ੱູ%֥ࠎԤഈđૌ࣮ఃٳљഈശބ༯ࢆ%ؓקࡎ֥႕ཙ,ࢲݔೂі5෮ൕğ і5ğಃᆣࡎ۬ؓႿڄག০ੱ֥ૹۋྟ ಃᆣࡎ۬ಃᆣࡎ۬ಃᆣࡎ۬ಃᆣࡎ۬ଆ čr=%Ďčr=%Ďଆ čr=%Ď čr=%ĎffffRW RW_GARCH_jump
RW_GARCH RW_GARCH_EWMA RW_TGARCH_jump RW_GARCH_M RW_GARCH_t RW_EGARCH RW_GARCH_M_t RW_TGARCH RW_TGARCH_t ၛഈᄎෘࢲݔіૼđڄག০ੱ֥טᆜؓקࡎࢲݔ႕ཙ҂նđඪૼಃᆣקࡎࢲݔ൳ڄག০ੱ֥႕ཙбࢠཬb ູਔॉҳܢௐࡎ۬ᆦӪؓקࡎࢲݔ֥႕ཙđૌٳљࡼܢௐ֥ᆦӪࡎ۬Ⴎ4ჭഈശ֞ჭބ༯ࢆ֞ჭѩ࠹ෘఃಃᆣࡎ۬đࢲݔೂі6෮ൕğ і6ğಃᆣࡎ۬ؓႿܢௐࡎ۬ᆦӪᆴ֥ૹۋྟ ಃᆣࡎ۬ಃᆣࡎ۬ಃᆣࡎ۬ಃᆣࡎ۬ଆ čS*=Ď čS*=Ďଆ čS*=Ď čS*=ĎRW RW_GARCH_jump RW_GARCH RW_GARCH_EWMA RW_TGARCH_jump RW_GARCH_M RW_GARCH_t RW_EGARCH RW_GARCH_M_t RW_TGARCH RW_TGARCH_t Ֆၛഈࢲݔটुđಃᆣࡎ۬ؓᆦӪࡎ۬э߄ࢠູૹۋđᆦӪࡎ۬эჭь߶ႄఏಃᆣࡎ۬ჭ֥эbંഈđೂݔؓಃᆣѓ֥ሧӁӵ୶၂۱หק֥ᆦӪࡎ۬đᄵ֒ᆃ۱ᆦӪࡎ۬एᆳྛࡎ۬ᄀ࣍đఃэطႄఏ֥ؓ௹ಃܙࡎ֥э߶ᄀૼཁb෮ၛđ࿊ᄴ၂۱ކൡ֥ᆦӪࡎ۬ቔູҕඔؓಃᆣ֥ሙಒקࡎ٤ӈᇗေb 5a ࢲݔҵၳٳ༅ࠣᆟҦࡹၰ ࡼૌ֥קࡎࢲݔđหљ൞๋ᄁଆ֥קࡎࢲݔ൧ӆࡎ۬бࢠđॖၛؿགྷ൧ӆࡎ۬აંࡎ۬ᆭࡗթᄝޓն֥ҵၳđЏۑಃᆣࡎ۬թᄝૼཁ֥ۚܙགྷའđթᄝбࢠᇗ֥൧ӆࠏđ҂০ႿݓࣁವစളӁ൧ӆ֥ࡲूؿᅚbٳ༅Ӂളҵၳ֥ᇅ؇ჰၹؓڿࣉބປݓ֥ሧЧ൧ӆđ՜ࣉࣁವစള൧ӆ֥ؿᅚऎႵᇗေ֥ၩၬb ൮༵đෙಖҐ౼ਔބ௹ಃ၂ဢ֥ٚمؓЏۑಪܢಃᆣࣉྛקࡎđ൞ѩ҂൞ᆇᆞ֥௹ಃӁđ൞Ⴎ܄ඳ෮ؿྛ֥ಪܢಃᆣđᄝؿྛਈഈ൞Ⴕཋ֥đ෮ၛఃࡎ۬ಸၞၹູ܂ܱ༢طФದູҠሺbطᆇᆞ֥௹ಃᄝؿྛਈഈ൞ીႵཋᇅ֥đࠧᆺေႵླđьିၛଖ۱ࡎ۬ܓઙ֞đ෮ၛࣼޓФದູҠሺbֻؽđݓಌكส০ࠏᇅؿߨቔႨ่֥ࡱbᄝಌكส০ࠏᇅ֥൧ӆᇏđم๙ݖؓ൧ӆࡎ۬ொ֥ۚ௹ಃࣉྛછॢطൈઙೆѓ֥ܢௐটൌགྷڄགส০đࣉط္ࣼمၹູ൧ӆᇏն؟ඔದ֥҂؎છॢط௹ಃ֥൧ӆࡎ݂۬߭֞ఃᆇൌࡎᆴഈಀb ࠎႿၛഈᇅ؇ྟჰၹ֥ٳ༅đૌಪູđݓႋھؿᅚᆇᆞ֥௹ಃ൧ӆđ๙ݖႵൌ৯֥ᇏࢺࠏܒԛᆇᆞ֥௹ಃӁđՖط۷ႵֹིؿᅚစളӁ൧ӆđࠇᆀ࣐ॖି֥ঔն൧ӆܿଆđิۚ൧ӆҠሺ֥ӮЧĠѩđႋ࣐ॹᄝ൧ӆഈႄೆછॢࠏᇅđԷᄯส০ࠏᇅؿߨቔႨ෮ླ่֥ࡱđҌିࣁವစളӁ֥ࡎ݂۬߭֞ఃކࡎ۬ഈb
6a ࢲં Ч໓ؓᇏݓܢಃٳᇂުഈ൧ؿྛ֥൮ᆦ܄ඳಪܢಃᆣiiЏۑಃᆣቓਔ༢֥קࡎ࣮bؓଢభӈႨ֥ᇙ؟ѯੱଆࣉྛൌᆣٳ༅֥ࠎԤഈđЧ໓০ႨHong & Li٤ҕඔଆഡקဒٚمđбࢠ۲۱ଆ֥ଆഡק༂ҵđ࿙ᅳԛଆഡק༂ҵቋཬ֥ଆbᄝᅧѓ֥ܢௐࡎ۬ѯੱหᆘᆭުđ০Ⴈหवઅଆඌؓఃಃᆣࣉྛקࡎb๙ݖؓЏۑܢٺܢௐѯੱ֥ٳ༅ၛࠣؓЏۑಃᆣ֥קࡎđૌ֤ԛၛ༯ࠎЧࢲંğ č1ĎЏۑܢௐ൬ၭੱѯթᄝૼཁ֥GARCHིႋa๋ᄁིႋၛࠣ٤ᆞྟđ҂ژކBSଆ֥ࡌഡđၹՎ҂ିᆰࢤᄎႨBSקࡎ܄ൔؓЏۑಃᆣקࡎđطсྶॉ੮ѓ֥ሧӁ൬ၭੱѯ֥ऎุหᆘb č2ĎᄝGARCHଆᇏႄೆ๋ᄁၹሰބҗҵtٳ҃नॖၛ֥ࢆ֮ଆഡק༂ҵb๋ᄁၹሰބҗҵtٳ֥҃ଆഡק༂ҵҵљ҂նbᇏݓܢௐ൧ӆ֥ᆟҦМࣟ۷ൡކა࿊ᄴ๋ᄁଆቔູЏۑಃᆣקࡎ֥ѓሙb č3Ď҂֥൬ၭੱѯଆ֥ಃᆣקࡎࢲݔթᄝбࢠն֥ҵၳđඪૼ࿊ᄴ၂۱ކൡ֥קࡎଆቔູѓሙؓ؎ఃކࡎᆴऎႵᇗေ֥ၩၬbطଆഡק༂ҵࠎЧཌྷ๋֥ᄁଆބҗҵtٳ҃ଆ֥קࡎࢲݔҵၳಏޓնđіૼđᄝູ၂۱စളӁ࿊ᄴކൡ֥ѯଆቔູקࡎѓሙൈđсྶࡼ࠹ਈٳ༅෮֤֥ࢲંൌ࠽౦ঃႵࠏ৳༢đҌି֤ԛбࢠॖौ֥ࢲંb č4Ďݓ֥ಃᆣࡎ۬թᄝૼཁ֥ۚܙđ൧ӆթᄝбࢠᇗ֥൧ӆࠏbఃᇅ؇ჰၹॖିႵਆ۱ğ൮༵ؿྛඔਈႵཋđಸၞФҠሺĠఃՑݓಌك൧ӆ֥છॢࠏᇅđીႵส০ࠏᇅؿߨቔႨ෮ླ่֥ࡱbູՎđૌࡹၰ൧ӆႄೆછॢࠏᇅđѩᇯ҄ࡹ৫ᆇᆞ֥௹ಃ൧ӆѩঔնࣁವစളӁ֥൧ӆܿଆđՖط۷ࡲूਅݺֹؿᅚݓ֥စള൧ӆb ҕॉ໓ངğ [1] Ball, C. A. and W. N. Torous, 1983, “A simplified jump process for common stock return”, Journal of Financial and Quantitative Analysis, 18, 53-65 [2] Black, F. and Scholes, M.,1973, “The pricing of option and corporation liabilities”, Journal of Political Economy, 81, 637-659. [3] Bollerslev T, 1986, “Generalised autoregressive conditional eteroskedasticy”, Journal of Econometrics, 31, 307-327. [4] Crouhy, M. and Galai, D., 1991, "Warrant valuation and equity volatility", In: "Advances in Futuresand Options Research", . Fabozzi (ed.), JAI Press Inc., page 203-215. [5] Das, S. R., 2002, “The Surprise Element: Jumps in Interest Rates”, Journal of Ecnometrics, 106, 27-65. [6] Duan, , The GARCH option pricing model, Mathematical Finance, 5, 13-32 [7] Engle, R F, 1982, “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation”. Econometrica, 50, 987-1007. [8] Engle, R. F., Lilien, D. M. and R. P. Robins, 1987, “Estimating time-varying premia in the term structure: the ARCH-M model”, Econometrica, 55, 391-407. [9] Galai, D. and Schneller, ., 1978, "Pricing of warrants and the value of the firm", The Journal of Finance, page 1333-1342. [10] Hong, Y. and H. Li., 2005, “Nonparametric Specification Testing for Continuous-Time
Models With Applications to Interest Rate Term Structures”, Review of Financial Studies, 18, 37-84. [11] Nelson, D. B, 1991, "Conditional Heteroskedasticity in Asset Returns: A New Approach." Econometrica, 59, 347-370. [12] Schulz, . and Trautmann, S., 1989, "Valuation of warrants - theory and empirical tests for warrants written on German stocks", Working Paper, University of Stuttgart (Germany), October 1989. [13]Schulz, . and Trautmann, S.,1994, "Robustness of option-like warrant valuation", Journal of Banking and Finance , page 841-859. [14] Vlaar, P. and F. Palm, 1993, “The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroskedasticity, and Jumps”, Journal of Business and Economic Statistics, 11, 351-60. [15] Zakoian, J-M, 1994, “Threshold Heteroscedastic Models”, Journal of Economic Dynamics and Control, 18, 931–955. [16] νྖđ౪đਟഒ܅đ1998đoᇏݓຓ߸൧ӆѯٳ༅pđu࠹࣮vđֻ1௹b [17] Ӊڌđ1999đo০Ⴈ݂߭-GARCHଆؓݓധܢ൧֥ٳ༅pđuყҩvđֻ4௹b [18] ఃૼđ࠱ᇑ༺đဗཫđ1998đoሱ่݂߭ࡱၳٚҵ (ARCH) ଆࠣႋႨpđuყҩvđֻ4௹b [19] ౄđ1994đo൧ӆႵིaᇛ௹ၳӈაܢࡎѯ—ؓഈݚaധᎪܢௐ൧ӆ֥ൌᆣٳ༅pđuࣜ࠶࣮vđֻ9௹b [20] ᄃӔđ2001đoഈݚܢ൧൬ၭੱGARCHଆቂ֥ൌᆣ࣮pđuඔਈࣜ࠶ඌࣜ࠶࣮vđֻ6௹b [21] ᅦනఅđઔېđಘđ2000đoܢௐ൧ӆڄགa൬ၭა൧ӆིੱ—ARMA-ARCH-Mଆpđuൗࢸࣜ࠶vđֻ5௹b
і2ğЏۑܢٺѯଆ֥ҕඔܙ࠹ࢲݔ RW RW RW RW RW RW RW RW RW RW RW ଆ RW GARCH EWMA TGARCHEGARCH GARCH-MGARCH TGARCH GARCH-MGARCH TGARCHGARCH-M Jump Jump Jump t t t ****µ -04 ***σ ****************α -05 -06 -06 -06 -06** ************************** *** α 1************************ *** β 1ϕ *** β 2*** λ ** δ ϑ *********γ *********c *********ν Log *****ᇿğč1Ďၹູږ෮ཋđીႵਙԛҕඔܙ࠹֥࠹ਈđᆺ۳ԛཁᇷྟࢲݔĠč2Ďіൕཁᇷྟඣູ1ĊĠіൕཁᇷྟඣູ5Ċb
